An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Mapping the language of science and science teaching practices : a case study of early childhood school science

Concerns raised in educational reports about school science in terms of students. outcomes and attitudes, as well as science teaching practices prompted investigation into science learning and teaching practices at the foundational level of school science. Without science content and process knowledge, understanding issues of modern society and active participation in decision-making is difficult. This study contended that a focus on the development of the language of science could enable learners to engage more effectively in learning science and enhance their interest and attitudes towards science. Furthermore, it argued that explicit teaching practices where science language is modelled and scaffolded would facilitate the learning of science by young children at the beginning of their formal schooling. This study aimed to investigate science language development at the foundational level of school science learning in the preparatory-school with students aged five and six years. It focussed on the language of science and science teaching practices in early childhood. In particular, the study focussed on the capacity for young students to engage with and understand science language. Previous research suggests that students have difficulty with the language of science most likely because of the complexities and ambiguities of science language. Furthermore, literature indicates that tensions transpire between traditional science teaching practices and accepted early childhood teaching practices. This contention prompted investigation into means and models of pedagogy for learning foundational science language, knowledge and processes in early childhood. This study was positioned within qualitative assumptions of research and reported via descriptive case study. It was located in a preparatory-school classroom with the class teacher, teacher-aide, and nineteen students aged four and five years who participated with the researcher in the study. Basil Bernstein.s pedagogical theory coupled with Halliday.s Systemic Functional Linguistics (SFL) framed an examination of science pedagogical practices for early childhood science learning. Students. science learning outcomes were gauged by focussing a Hallydayan lens on their oral and reflective language during 12 science-focussed episodes of teaching. Data were collected throughout the 12 episodes. Data included video and audio-taped science activities, student artefacts, journal and anecdotal records, semi-structured interviews and photographs. Data were analysed according to Bernstein.s visible and invisible pedagogies and performance and competence models. Additionally, Halliday.s SFL provided the resource to examine teacher and student language to determine teacher/student interpersonal relationships as well as specialised science and everyday language used in teacher and student science talk. Their analysis established the socio-linguistic characteristics that promoted science competencies in young children. An analysis of the data identified those teaching practices that facilitate young children.s acquisition of science meanings. Positive indications for modelling science language and science text types to young children have emerged. Teaching within the studied setting diverged from perceived notions of common early childhood practices and the benefits of dynamic shifting pedagogies were validated. Significantly, young students demonstrated use of particular specialised components of school-science language in terms of science language features and vocabulary. As well, their use of language demonstrated the students. knowledge of science concepts, processes and text types. The young students made sense of science phenomena through their incorporation of a variety of science language and text-types in explanations during both teacher-directed and independent situations. The study informs early childhood science practices as well as practices for foundational school science teaching and learning. It has exposed implications for science education policy, curriculum and practices. It supports other findings in relation to the capabilities of young students. The study contributes to Systemic Functional Linguistic theory through the development of a specific resource to determine the technicality of teacher language used in teaching young students. Furthermore, the study contributes to methodology practices relating to Bernsteinian theoretical perspectives and has demonstrated new ways of depicting and reporting teaching practices. It provides an analytical tool which couples Bernsteinian and Hallidayan theoretical perspectives. Ultimately, it defines directions for further research in terms of foundation science language learning, ongoing learning of the language of science and learning science, science teaching and learning practices, specifically in foundational school science, and relationships between home and school science language experiences.

Early years teachers’ attitudes towards mathematics

Worldwide, there is considerable attention to providing a supportive mathematics learning environment for young children because attitude formation and achievement in these early years of schooling have a lifelong impact. Key influences on young children during these early years are their teachers. Practising early years teachers‟ attitudes towards mathematics influence the teaching methods they employ, which in turn, affects young students‟ attitudes towards mathematics, and ultimately, their achievement. However, little is known about practising early years teachers‟ attitudes to mathematics or how these attitudes form, which is the focus of this study. The research questions were: 1. What attitudes do practising early years teachers hold towards mathematics? 2. How did the teachers‟ mathematics attitudes form? This study adopted an explanatory case study design (Yin, 2003) to investigate practising early years teachers‟ attitudes towards mathematics and the formation of these attitudes. The research took place in a Brisbane southside school situated in a middle socio-economic area. The site was chosen due to its accessibility to the researcher. The participant group consisted of 20 early years teachers. They each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow, 2005), which is a 40 item instrument that measures attitudes across the four dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The teachers‟ total ATMI scores were classified according to five quintiles: strongly negative, negative, neutral, positive and strongly positive. The results of the survey revealed that these teachers‟ attitudes ranged across only three categories with one teacher classified as strongly positive, twelve teachers classified as positive and seven teachers classified as neutral. No teachers were identified as having negative or strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of attitudes were selected from the original cohort to participate in open-ended interviews to investigate the formation of their attitudes. The interview data were analysed according to the four dimensions of attitudes (value, enjoyment, self-confidence, motivation) and three stages of education (primary, secondary, tertiary). Highlighted in the findings is the critical impact of schooling experiences on the formation of student attitudes towards mathematics. Findings suggest that primary school experiences are a critical influence on the attitudes of adults who become early years teachers. These findings also indicate the vital role tertiary institutions play in altering the attitudes of preservice teachers who have had negative schooling experiences. Experiences that teachers indicated contributed to the formation of positive attitudes in their own education were games, group work, hands-on activities, positive feedback and perceived relevance. In contrast, negative experiences that teachers stated influenced their attitudes were insufficient help, rushed teaching, negative feedback and a lack of relevance of the content. These findings together with the literature on teachers‟ attitudes and mathematics education were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes Towards Mathematics. This model explains positive and negative influences on attitudes towards mathematics and how the attitudes of adults are passed on to children, who then as adults themselves, repeat the cycle by passing on attitudes to a new generation. The model can provide guidance for practising teachers and for preservice and inservice education about ways to foster positive influences to attitude formation in mathematics and inhibit negative influences. Two avenues for future research arise from the findings of this study both relating to attitudes and secondary school experiences. The first question relates to the resilience of attitudes, in particular, how an individual can maintain positive attitudes towards mathematics developed in primary school, despite secondary school experiences that typically have a negative influence on attitude. The second question relates to the relationship between attitudes and achievement, specifically, why secondary students achieve good grades in mathematics despite a lack of enjoyment, which is one of the dimensions of attitude.

Engineering-based modelling experiences in the elementary classroom

Introducing engineering-based model-eliciting experiences in the elementary curriculum is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results indicate that engineering model-eliciting activities can be introduced effectively into the elementary curriculum, providing rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Thinking Critically in the Land of Princesses and Giants : The Affordances and Challenges of Critical Approaches in the Early Years

During the last four decades, educators have created a range of critical literacy approaches for different contexts, including compulsory schooling (Luke & Woods, 2009) and second language education (Luke & Dooley, 2011). Despite inspirational examples of critical work with young students (e.g., O’Brien, 1994; Vasquez, 1994), Comber (2012) laments the persistent myth that critical literacy is not viable in the early years. Assumptions about childhood innocence and the priorities of the back-to-basics movement seem to limit the possibilities for early years literacy teaching and learning. Yet, teachers of young students need not face an either/or choice between the basic and critical dimensions of literacy. Systematic ways of treating literacy in all its complexity exist. We argue that the integrative imperative is especially important in schools that are under pressure to improve technical literacy outcomes. In this chapter, we document how critical literacy was addressed in a fairytales unit taught to 4.5 - 5.5 year olds in a high diversity, high poverty Australian school. We analyze the affordances and challenges of different approaches to critical literacy, concluding they are complementary rather than competing sources of possibility. Furthermore, we make the case for turning familiar classroom activities to critical ends.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Anglican boarding school a hotbed of sexual punishment

THE little Anglican boarding school of St Barnabas, in the misty mountain town of Ravenshoe, north Queensland, was allegedly a hotbed of physical and sexual abuse in the 1960s. North Queensland Bishop Bill Ray has confirmed the diocese has few files about the school -- which was closed mid-term in 1990 -- with suspicions they were dumped "down a well or an old mine shaft" in the district A history of brutal physical punishment and sexual abuse at the school dating from the 1960s is now emerging. Headmaster Robert Waddington, who arrived at the school from England to be headmaster in 1961, dished out daily canings to many of his young students and then allegedly raped some behind closed doors in his room or the sick bay, which were next to each other. Former St Barnabas student Bim Atkinson, now 58, and two other former students have levelled allegations against the man they called "the Wadd".

Book review "Moving Innovation: A History of Computer Animation by Tom Sito , The MIT Press: Cambridge, MA, 2013"

As a Lecturer of Animation History and 3D Computer Animator, I received a copy of Moving Innovation: A History of Computer Animation by Tom Sito with an element of anticipation in the hope that this text would clarify the complex evolution of Computer Graphics (CG). Tom Sito did not disappoint, as this text weaves together the multiple development streams and convergent technologies and techniques throughout history that would ultimately result in modern CG. Universities now have students who have never known a world without computer animation and many students are younger than the first 3D CG animated feature film, Toy Story (1996); this text is ideal for teaching computer animation history and, as I would argue, it also provides a model for engaging young students in the study of animation history in general. This is because Sito places the development of computer animation within the context of its pre-digital ancestry and throughout the text he continues to link the discussion to the broader history of animation, its pioneers, technologies and techniques...

How talk and interaction unfold in a digitally enabled preschool classroom

The use of mobile digital devices, such as laptops and tablets, has implications for how teachers interact with young students within the institutional context of educational settings. This article examines language and participation in a digitally enabled preschool classroom as students engage with teachers and peers. Ethnomethodology, conversation analysis and membership categorization analysis are used to explicate video-recorded episodes of students (aged 3-5 years) interacting while using a laptop and a tablet. Attending to the sequential organization (when, how) and the context relevance (where) of talk and interaction, analysis shows how the intersection of interactions involving the teacher, students and digital devices, shape the ways that talk and interactions unfold. Analysis found that the teacher-student interactions were jointly arranged around a participation framework that included: 1) the teacher’s embodied action that mobilizes an accompanying action by a student, 2) allocation of turn-taking and participation while using a digital device and, 3) the affordances of the digital device in relation to the participants’ social organization. In this way, it is possible to understand not just what a digital device is or does, but the affordances of what it makes possible in constituting teachers’ and students’ social and learning relationships.

Heterosexual and nonheterosexual young university students’ involvement in traditional and cyber forms of bullying

Research has consistently found that school students who do not identify as self-declared completely heterosexual are at increased risk of victimization by bullying from peers. This study examined heterosexual and nonheterosexual university students’ involvement in both traditional and cyber forms of bullying, as either bullies or victims. Five hundred twenty-eight first-year university students (M= 19.52 years old) were surveyed about their sexual orientation and their bullying experiences over the previous 12 months. The results showed that nonheterosexual young people reported higher levels of involvement in traditional bullying, both as victims and perpetrators, in comparison to heterosexual students. In contrast, cyberbullying trends were generally found to be similar for heterosexual and nonheterosexual young people. Gender differences were also found. The implications of these results are discussed in terms of intervention and prevention of the victimization of nonheterosexual university students.